Spring 2016

Published by the Courant Institute of Mathematical Sciences at University Courant Newsletter Lai-Sang Young on the mathematics of chaos and modeling the dynamical brain Volume 12, Issue 2

p02 p08 IN MEMORIAM: Norman Grossman

p06 FINDING THE PATH TO WELLNESS David Sontag on how artificial intelligence is transforming healthcare

p04 HOLOGRAMS IN THE MATERIAL WORLD with Pierre-Emmanuel Evreux (M.S. ‘03)

ALSO IN THIS ISSUE:

BOGOMOLOV AND LIKE FAMILY: KHOT NAMED 2015 LARRY COHEN, SILVER PROFESSORS TIRELESS STAFF p08 MEMBER, RETIRES p12 FACULTY HONORS p10 A LOT OF HEART: TAMAR ARNON, MATH OUTREACH STUDENT ADVOCATE, CHAMPION: RETIRES FRED GREENLEAF p13 RETIRES, BUT DOESN’T SLOW DOWN PUZZLE: SLEEP NO p11 MORE Image: Neurons of the cerebral cortex. p14 Lai-Sang Young on the mathematics of chaos and modeling the dynamical brain

by April Bacon

Signatures of chaos “Everybody thinks they know chaotic behavior when they attractor solutions are chaotic in the sense that the trajectories see it, but there’s no definition people agree on, and I doubt that of two nearly identical points on the attractor will widely and there can be a single definition that captures everything we want it quickly diverge. One of the biggest realizations in the theory of to be,” says Lai-Sang Young, world-renowned expert in dynamical chaotic systems over the past fifty years, says Lai-Sang, is that systems, Henry & Lucy Moses Professor of Science, and Professor even when everything is determined by equations and nothing is of Mathematics and Neuroscience at NYU. left to chance, chaotic systems can produce data that are virtually Disorder (known colloquially as “chaos”) and order (such indistinguishable from those of random processes (such as as the predictable swing of a pendulum) make up the two ends of flipping a coin). the spectrum of dynamical systems, a research field that seeks to understand how a system evolves over time. Dynamical systems can be found everywhere in nature, in neural networks, ecosystems, weather, financial markets, manmade structures, and in the mathematical equations and algorithms developed to model these processes. “You can see that it’s kind of connected to everything,” says Lai-Sang. While Lai-Sang doesn’t believe there is a precise definition for the term, she says “there are signatures of chaos.” A framework she has laid out identifies three such signatures: hyperbolicity, a geometric measure of instability; entropy, from information theory; and decay of time correlations, from probability theory. These three signatures can roughly be equated to asking: Just how sensitively does a system depend on its initial conditions (hyperbolicity)? Does knowledge of a system’s past offer enough information to predict its future (entropy)? And, Image 1 how quickly is the system losing its memory (correlation decay)? The more sensitive, the less predictable, and the quicker the Strange attractors are really messy objects, and it helps memory loss, the more chaotic. These ideas are not just intuitively to have simple examples. Shear-induced chaos, a particularly but also formally related, and Lai-Sang has helped put some of that simple instance of which is shown above (Image 1), is one of on firm mathematical footing. the very few paradigms of chaos theory where there is a well- developed mathematical theory with rigorous proofs, thanks to Strange attractors of the simplest kind the work of Lai-Sang and collaborator Q.D. Wang (University of The well-known example of Edward Lorenz’s butterfly Arizona). They built on the seminal work of Michael Benedicks (see image on back cover) comes from a model of atmospheric and Lennart Carleson, who analyzed a special system called the convection abstracted down to just three variables that depend on Hénon map. Using the techniques offered in this one instance, each other in a non-linear way. Think of the three variables as the Lai-Sang and Wang built a general theory of what they call coordinates of a as it flies around — the path, or trajectory “strange attractors of the sim plest kind,” or, more formally, “rank- the gnat takes is the solution to the equations. In Lorenz’s model, one attractors.” All attractors are very complex, but this kind is the path always traces out a compact pattern, called an “attractor” the simplest of strange attractors, as it has only one direction of (which in this case looks like a butterfly). Even with just three instability, and has been shown to appear right after a system variables, there is no analytical solution, so a computer must be loses stability. used to solve the equations. If you start your program with two “Though I didn’t know about it, an example similar to the different initial states, the computed solutions will take completely one shown was studied numerically by the late George Zaslavsky, different paths on the attractor, even if their starting conditions an NYU physicist, many years earlier. The idea is very simple,” differ by only a miniscule amount. This is what “sensitive says Lai-Sang. At t=0, a periodic attractor (grey circle) attracts dependence on initial conditions” means — every solution lies on everything around it into its orbit; orbits outside of the circle the attractor, but the path taken along it is never the same. move slightly faster than those inside, creating some shear. The As Lai-Sang explains, attractors are “stabilizing” because they system is then “kicked” to the right (blue circle), and allowed to draw a large number of initial conditions toward a relatively small settle back toward its original state. During this time, the shear region of the solution space. Yet the dynamics of models that have acts on different parts of the blue circle differently, resulting

2 — CIMS Newsletter, Spring 2016 Image 2 These “raster-plots” show the spiking activity of more than 400 neurons in a local population, taken from the model of the primary visual cortex in Lai-Sang’s current project with Professor Robert Shapley and Ph.D. student Logan Chariker. The vertical axis is neuron number, and the horizontal axis is time. The top panel shows background activity, and the bottom panel shows what happens when the model cortex is stimulated.

in the development of the ‘tail’ clearly visible at time t=3. The fold “For large systems, characterizations of chaos that work solidifies between t=3 and t=6 as the entire structure is attracted back for systems with few degrees of freedom may not be so relevant to the grey circle. This process is repeated once every 6 units of time. — often it is not even clear exactly what chaos means. A much The stretch-and-fold leads to the formation of a strange attractor, more important goal in studying large systems is to identify and displaying the three above-mentioned signatures of chaos. understand emergent phenomena,” Lai-Sang explains. In the brain, the organization of grouped neurons together cause behaviors The Dynamical Brain to ‘emerge’ that are different from and beyond those exhibited “The brain is one big dynamical system, maybe the most by individual neurons. Emergent behaviors are characteristic of fascinating one of all,” says Lai-Sang. “In addition to being a very complex dynamical systems. large and complex dynamical system,” she elaborates, “[it] does not One such collective behavior (as seen in Image 2) is the operate in isolation: It is constantly receiving input from the external tendency of excitatory and inhibitory neurons to fire in clusters. world and from the rest of the body. As a dynamical system, it is ‘out In the image, a dot represents a neuron spike — red for excitatory of equilibrium.’” neurons and blue for inhibitory ones. The bottom panel shows In collaboration with Robert Shapley of NYU’s Center for that when the model cortex is stimulated, seemingly random Neural Science, she is studying the dynamics of the primary visual subgroups of neurons fire near-synchronously in a semi-regular cortex (V1). Central to our ability to comprehend visual information, rhythm within the gamma range (40-70 Hz). “Individual neurons V1 is one of the few areas of the brain for which a large amount of spike irregularly, and if you watch one neuron there’s no reason to experimental data already exists, due in part to its accessible location predict that together they will produce this rhythm,” says Lai-Sang. in the occipital lobe. A primary goal of this research is to build a “What happens is that when a few excitatory neurons start to fire, model that behaves like the real brain, meaning it produces outputs this tends to cause more of them to become excited; it’s called that resemble experimental data, so that it can be used to answer ‘recurrent excitation.’ And then at the same time the inhibitory questions about the real brain — it is far easier to run simulations ones get excited, until at some point the inhibitory neurons step in on a model than to run tests on the actual brain! Another goal is to and push everything back. …The rhythm comes from this push- develop further paradigms for understanding dynamical systems. and-pull kind of phenomenon. Any group of neurons hooked Although still very much in the purview of dynamical systems, together will automatically start to form these patterns—and no this work is different from the attractors mentioned above in some matter what you do, you can’t get rid of it, even if you try!” In some notable ways, including the constant input and the size. The scale of earlier modeling work, Lai-Sang and her collaborator Adi Rangan, the object of study is vastly larger: “We have 1011 neurons in the brain,” also of Courant, first discovered these push and pull patterns. says Lai-Sang. “You don’t study all of them — you study just a tiny It turns out to match very well what people have observed in piece of the brain, but even that tiny piece can have a million or more experiments. neurons.” Also, the rules of operation of the system are unknown for “The diversity of behaviors in neuronal models is also the brain, and a major part of the research is to deduce these rules an emergent phenomenon,” says Lai-Sang. “You program from the brain’s outputs. the neurons to be more or less the same, but through their In terms of the above signatures of chaos, the questions need interactions they start to take on completely different properties.” reframing. For example, it makes sense to ask how quickly cortical Lai-Sang and collaborators have mostly finished modeling response diverges for small changes in the initial cortical state or the input layer of V1. “I’m pretty sure we can go further in the stimuli, but this question itself immediately raises another question: visual cortex,” she says. “The deeper into cortex we get, the more “How do we measure the distance between cortical states? In a system ambiguous the situation will become, as there will not be enough that describes the interaction of hundreds of thousands of neurons, data to tie the model down. The visual cortex is part of the cerebral not every detail will carry weight,” explains Lai-Sang, “and some cortex, a very thin sheet only about two millimeters thick that amount of coarse-graining, or lumping, is necessary.... The challenge wraps all the way around the brain. It’s mostly the thinking part of is to devise a meaningful metric that captures system attributes the brain. We hope to generalize some of our work on V1 to other relevant to the investigation.” areas of the cortex and that’s where I would eventually like to go.”

3 Dynamical systems is evolving Lai-Sang sees the task of dynamical systems research for the 21st century as making these kinds of connections to other disciplines, and to other fields of mathematics. “The field itself is evolving—it’s not just that it’s about evolving things,” she says. But the movement of some dynamical systems research from the theoretical to the applied — such as Lai-Sang’s work on the brain — is not a one- way street. “There are many questions that I want to take back to dynamical systems theory,” says Lai-Sang, from broad questions such as “How do you analyze large dynamical systems made up of lots of small constituent subsystems (such as individual neurons) coupled together?” to “How do you develop a dynamical theory of systems in which two competing groups of agents play against each other, like excitatory and inhibitory neurons?” Lai-Sang Young (center) stands outside of Warren Weaver Hall with Pure and applied mathematics “feed off of each other,” she finishing Ph.D. students Alex Blumenthal (left) and Logan Chariker. Alex has been awarded an NSF Postdoctoral Fellowship, and Logan a says, “and Courant is the best place in the whole world for fostering Swartz Foundation Fellowship. the entire spectrum. That’s very special about Courant. That’s the reason I came. You know that, right? Courant is really special.” n

Holograms in the Material World Pierre-Emmanuel Evreux and LEIA 3D’s mission for consumer holographics

by April Bacon

In 2013, Courant physics. When they graduated in 2001, firm’s money directly into the market. alumnus Pierre- both were eager for a new experience and His focus was on understanding all of a Emmanuel to come to the U.S., says Evreux. Fattal company’s securities (corporate bonds, Evreux (M.S., chose Stanford on the West coast, while equity, etc.) in isolation as well as in Mathematics Evreux chose Courant on the East. relation to one another—in order to in Finance, ‘03) “The reason I chose NYU was judge how they might perform within the travelled from for the quality of its professors and the current macroeconomic environment. his home in intersection with Wall Street,” says Evreux. The experience gave the future start- New York to Palo “When you study applied math dedicated to up co-founder a clear picture of what Alto, California to visit longtime friend a certain field, you always want a balance fundamental ingredients make up a David Fattal. There, Fattal revealed to between those two worlds. And Courant strong and scalable company, how a Evreux a prototype for a new technology: is doing a great job at this. So that’s why company raises funds, as well as the a flat, transparent panel, about 2 inches I went to NYU. And obviously New York many ways a company can shape itself in diameter, above which floated a always played a part in it!” in regard to its core operations and what holographic ‘x’ and ‘o,’ smoothly While enrolled at Courant, Evreux it will accomplish by partnerships. “One appearing in three dimensions to the was also working part time at JWM of the main things I got from finance,” naked eye. By December of that same year, Partners, a hedge fund in Greenwich, Evreux adds, “is thinking in terms of Evreux, Fattal, and third co-founder Zhen Connecticut. “I wanted to gain as much risk and optionality. Risk taking is Peng had formed LEIA 3D, with the goal of experience and practical knowledge as I an essential ingredient in building a making holographic technology a mass- could,” he says, and after graduating from company and you don’t really learn market reality. Courant he continued in that role before it in any other industry. I really thank taking a position at Morgan Stanley as a investing for that.” From trading desk to start-up portfolio manager in ’04. He worked seven In 2011, Evreux left Citigroup The genesis of that partnership years with the same group as they served and spent a few years as Managing began over a decade before, when Morgan Stanley, then left that company Director of Corporate Credit at Hutchin Evreux met Fattal while enrolled at Ecole to form their own hedge fund—Old Lane Hill Capital before he went on his Polytechnique. Evreux was studying Partners, later bought by Citigroup. fateful visit to see Fattal, who was then finance and applied math, and Fattal With this group, Evreux invested the a Research Scientist at Hewlett-Packard

4 — CIMS Newsletter, Spring 2016 with content in the future.” The approach is in contrast to virtual reality, which requires the user to wear a headset. “With the VR approach, you sit in your living room with a large headset on and you get a very immersive experience which is centered around you. What LEIA is saying is, that’s great when you’re at home and you want that immersive experience, but how can you access these virtual worlds when you’re in the street, in your car, or with friends?” By bringing the digital world into the material — rather than the individual into the virtual — “holographic reality” doesn’t impair mobility or social interactions, explains Evreux. Image 1 The vision for the technology includes applications across a number of industries. Imagine, in medicine, viewing Laboratories in Palo Alto. After the big from different positions in space. Upon an ultrasound of an unborn baby in three reveal, “I was very much interested in looking at a LEIA display, the observer’s dimensions, projected above a device the start-up adventure,” says Evreux. “I right and left eye will naturally perceive held in the palm of a hand; in cell phones, had looked at companies for close to different images and experience a 3D the holographic presence of a loved-one fifteen years. That experience gave me the stereoscopic sense of depth (akin to the states or countries away in “holochat” or opportunity to create my own company glasses-based 3D effect experienced 3D selfies; and in e-commerce, viewing a based on what I think are the soundest at the movie theater). Moreover, when product for sale from every angle. Evreux principles. the observer moves around the display, says after the the company was launched, “And I always like to work with friends different pairs of views will be presented the first inquiries they received were from — it makes the adventure more fun.” to his or her eyes to achieve a full “motion doctors interested in the technology’s parallax” effect — or the ability to see ability to give surgeons a sense of depth. Holograms you can touch around objects. And there has naturally been a big In just over two years, LEIA 3D With the goal to integrate the response from game developers as well. has deployed development kit versions technology into everyday life as seamlessly “You can imagine angry birds with the birds of its display to corporate and individual as possible, LEIA is taking their displays popping out of your display,” says Evreux. developers, and is scheduled for the first two steps further. In partnership with “Most games today are being programmed market release of its holographic display in other technology developers, the company in 3D but they’re being shown in 2D. So we consumer smart phones and automotive has already developed a demonstration of can actually show on our display all these navigation systems by the end of 2017. their display to include hover touch — a games already.” The technology is as striking as the vision way to interact with the digital object by “Building a company from scratch LEIA 3D has laid out for it. In a classic directly “touching” the hologram, rather is a lot of work,” he says, “but it’s a hologram, the 360-degree form of an object than the screen. And in other partnerships fascinating experience because it’s the is reconstructed by a complex pattern of they are working to integrate haptic combination many things. It’s technology, light projected and interfering with itself at feedback, an ultrasound-based technology it’s nanofabrication, it’s business many points, an arrangement too complex that will simulate for users not only the development, it’s software, it’s content, it’s to allow for projection of an object at video ability to touch, but to feel the hologram. supply chain, it’s marketing, it’s intellectual speeds. LEIA simplifies the holographic They are hoping to have a demonstration property.” And, of course, “it’s finance.” At rendering process and achieves a video- which includes haptic feedback by the end present, LEIA has assembled a team of 25, rate holographic effect by using a layer of of the year. These three things packaged each with varying expertise in these areas. nanotechnology (the size of a single hair together — the hologram, hover touch, “It’s a very exciting period,” says Evreux. divided by a thousand) underneath an and haptic feedback — constitute what “And that’s why I decided to move to the LCD panel (see Image 1). Light from the LEIA describes as “holographic reality.” West Coast. I miss New York a lot. But it’s backlighting unit interacts with a nano- “We have this catchy phrase which worth it.” n grating system that “diffracts” light in many basically says we are materializing the directions, creating a “lightfield” with 64 digital world,” says Evreux, “and we think different images observable simultaneously this is the new way people will interact

5 Finding the path to wellness David Sontag on how artificial intelligence is transforming healthcare

by April Bacon

got a kick out of looking at your work just now. Here’s a project that I ran in the 1970s and 80s. It should look very familiar’! “The goals and the approaches taken back in the 70s were quite similar,” says David. “There are new technologic improvements, but what’s largely changed is the timing. Now we, number one, have electronic health data that is widely available for research and operations purposes and two, we have computers that are by the bedside.” The feedback loop for those doing medical diagnosis algorithms in the 70s was much longer, explains David: After questioning the patient, the researcher would have to run David Sontag and his group in front of the arch. Top: Yacine Jernite, to the mainframe computer in another area of Rahul Krishnan, Uri Shalit, Carlos Guzman, Ankit Vani. Bottom: Justin Mao-Jones, Maya the hospital — such as the basement — type Rotmensch, David Sontag, Narges Razavian, Rachel Hodos, Aarti Bagul. in patient responses, wait for the computer’s In the near future, algorithms running “There’s nothing magical about this,” output, return to bedside and repeat. In the autonomously behind the scenes will inform he explains. “It’s really just about doing fast-paced hospital environment, this made healthcare practitioners by preparing an things the way they should be done…But AI impractical to implement. Now that loop is intelligent summary of each patient admitted the problem is that the clinical team doesn’t significantly faster. to the hospital, says David Sontag, Assistant have time, and especially in the United “Having the data and having computers Professor of Computer Science at Courant, States, clinicians are managing way too gets us a large chunk of the way there,” says whose focus of research is on machine many things.” David. “It opens the door but it doesn’t solve learning problems for healthcare. The In the longer term, David envisions all the problems. There are still some major algorithms will reason about the patient’s that machine learning will make healthcare challenges.” health, presenting a summary of what is more proactive than reactive, with patients currently going on with the patient along participating more in their own care through The data: noisy, incomplete, with what it believes to be relevant from the apps and websites. “If one can extremely mismatched, and biased patient’s past medical history. David says cheaply and easily get a blood test that can Data for each patient is housed inside the historical information “could provide measure hundreds of different biomarkers of his or her Electronic Health Record (EHR). essential context which could change for a few cents, and that data is made The data in EHRs, however, is unstructured and treatment decisions.” readily available to algorithms, then we noisy, and this is one of the biggest challenges Algorithms will always be thinking don’t necessarily need to wait until we see a in machine learning today: how to build behind the scenes to keep track of patients patient exhibiting signs of diabetes in order algorithms that can structure, circumvent, or by, for example, detecting if a patient is “on to recognize that they’re on a trajectory to otherwise work on top of noisy data. a trajectory toward clinical deterioration becoming diabetic. We don’t have to wait There are many ways in which the data early on and alerting the clinical team.” The until someone develops a large tumor to is messy. For example, it is heterogeneous: Lab algorithms will be able to prompt physicians recognize that they have a cancer.” results, medical diagnostic codes, and clinical if a prescribed drug doesn’t match up notes can all be a part of a patient’s EHR. The with what has been prescribed to similar A unique moment data is imperfect: text may refer to a single patients, or if a symptom is added to a “The set of questions that people are condition with many different descriptive patient’s medical record which “looks like an hoping to solve with healthcare and AI are terms. There may be bias in the data, such as anomaly.” In the latter example, the quality not new,” says David. “And there were very which specific diagnosis code is assigned (often of the data is improved with minimal effort smart people that were tackling them 40 the one that pays the most); and the data may by practitioners; and in the former, Artificial years ago.” have entry errors or be otherwise incomplete. Intelligence (AI) is employed for “preventing Before David gave a talk in November Machine learning algorithms can work with simple mistakes, which happen every single at Stanford, he received an email from this data, learning and improving a model over day and lead to a lot of the heartbreak in a former AI researcher who saw the talk time — but it creates one of the challenges healthcare,” says David. announcement. The email said: “‘Hi, David. I David and his team have been working to

6 — CIMS Newsletter, Spring 2016 also transferable to other institutions — because it has organized EHR data using anchors, which are observed variables that are linked to a hidden “parent” variable. For example, two anchors for the parent variable diabetes include diagnosis code 250.xx and a medication history of diabetic therapy. Barring possible entry error, either of these Image 1: Probabilistic model used to infer clinical state variables (top) from observed clinical appearing in a patient’s EHR make it pretty data (bottom). Semi-supervised learning is able to recover the model from data in which the top likely the patient has diabetes. However, variables’ values are hidden so long as a domain expert specifies one or more “anchors” for each no assumptions are made about what hidden variable. the absence of the anchors implies about overcome: transferability. There is a “cold ER and used machine learning to help the parent variable. David refers to these start” problem of transferring the algorithms automate the documentation process.” anchors as “noisy labels” as they do not label from one population to another. Applied to It works like this: Instead of the data directly, but link data together in a a different hospital’s population, algorithms immediately assigning a chief complaint to predictive way. which are not transferable will have to learn a patient who walks into the ER, the nurse The algorithms are “semi-supervised” the structure of the new hospital’s data first talks to the patient and writes a twenty- because they require some manual input from scratch. to fifty-word assessment including vital in order to add structure to the data — the Building algorithms that can work on signs, symptoms, and reasons for the visit. clinical team “supervises” the system by top of noisy data is “one of the last few things That data — plus historical data if available suggesting anchors, and the algorithms learn that need to be solved in order for AI to have — is processed by the algorithm to predict the rest of the model autonomously. “As long a big impact in healthcare,” says David. the top five possible chief complaints, one as we can catch at least one of the ways that of which is then selected by the nurse. A text a condition is often mentioned, that’s good Finding the path to wellness box is also available for manually entering a enough,” says David. “The other ways that it The team already has different complaint, which has a contextual could be mentioned are automatically learned implementations of their algorithms in autocomplete similar to those used by many by the algorithm.” place in several clinical environments. At internet search engines. David and his team have been Beth Israel Deaconess Medical Center’s He and his team rolled out the system developing many other algorithms and Emergency Room (in Boston), systems slowly, further optimizing and automating systems that also integrate machine learning that inform clinical decisions, save time, it based on how it was being used and was into healthcare by, for example, making AI and reduce the chance of error are already performing in the real environment. “We better at checking symptoms and diagnosing running for all 60,000 patients who use ER created a plot where you could see, over the conditions, pinpointing which tests are services there each year. course of one year, how the quality of the most likely to lead to a diagnosis, and In one implementation, the team has chief complaints got better and better,” he identifying which patients are most at risk for improved the quality of chief complaints in says, “until, by one metric, it reached 100 developing certain diseases — all outcomes the ER. Chief complaints — such as chest percent. That’s likely our biggest success which improve patient care and maximize pain, cough, or pain in left arm — are taken case because it’s being used for every single prevention in a cost-effective manner by when a patient is admitted and displayed patient that comes into the ER today at that targeting the right patients. along with name, age, and bed number on hospital — for about two years now.” “The last five years that I’ve been at a big screen for the clinical team to see. In another implementation used NYU, I’ve been digging deep into healthcare, “The better the quality of that information, for all of the hospital’s ER patients, understanding the fundamental problems, the more useful it is for keeping track of electronic health records are being used and then generalizing back to computer patients and understanding who might “to continuously predict in real time about science,” summarizes David. “I’ve been be critical,” David says. That data is also 40 or 50 different clinical state variables,” figuring out what are the theoretical questions used for enrolling patients in clinical trials, says David. “These include abdominal pain, that, if we solve them, will directly affect and for retrospective clinical research alcoholism, allergic reaction, ankle fracture, healthcare, and also so many other fields. such as assessing effectiveness of certain diabetes, deep vein thrombosis, kidney “But it’s the healthcare part which interventions and building risk stratification stone, HIV, geriatric fall,” etc. is really guiding my work. There are many algorithms to help identify patients who are If the algorithm predicts cellulitis, for interesting theoretical questions to study in most at risk for certain diseases. instance, it will ask if the practitioner wants machine learning and which ones I tackle Utilizing a new ontology for the to enroll the patient in a clinical pathway for are guided by the ones that I think are most complaints — which was developed by Beth that infection. This system helps to ensure urgent in healthcare,” he says. “My hope is Israel’s Steven Horng, MD, with help from that care is standardized and that clinical that, if I succeed with my research, I’m going David and his team, and which they hope pathways are not forgotten. to ultimately save or improve people’s lives. will eventually be implemented nationwide The algorithm is able to identify That’s what drives my work.” n — the team “changed the workflow in the and trigger clinical pathways — and is

7 Fedor Bogomolov and Subhash Khot named 2015 Silver Professors

Congratulations to Fedor and Subhash Bogomolov conjecture about Galois orbits of hard are problems to solve or approximate? for being named Silver Professors! A bit points on abelian varieties — these are just For over three decades, the main approach about the work of each, as included in the a few of his deep ideas, which continue to to this question was through NP-hardness: announcement by Gérard Benarous, Director inspire researchers worldwide. Fedor’s most namely, we provide strong evidence for the of the Courant Institute of Mathematical recent work, on almost abelian anabelian hardness of a problem by showing that it is Sciences and Thomas Carew, Dean for the geometry, unraveled hidden structures in as hard as any other problem in the class NP. Faculty of Arts & Science: function fields of algebraic varieties, allowing Assuming that NP contains hard problems, Fedor Bogomolov has contributed the reconstruction of these fields from their as most experts strongly believe, we deduce fundamental insights to a wide range of Galois symmetries. This is a tremendously that our problem is hard. This paradigm fields, from his early papers in topology, significant development, creating a whole has been extremely fruitful and has led to a differential and algebraic geometry, to new philosophy in higher-dimensional complete understanding of some important number theory, group theory, invariant birational geometry. combinatorial optimization problems. Yet, a theory and many others. His decomposition Fedor has published more than large number of problems did not succumb theorem is the basis of classification of 110 papers, given plenary talks at major to this approach, and their hardness varieties and forms the foundation of modern international meetings, and served on remained a mystery for many years. string theory and mirror symmetry, some editorial boards of leading mathematical Subhash’s Unique Games conjecture of the most important concepts in modern journals. He is one of the giants of modern (UGC), introduced in his ingenious 2002 mathematical physics. It is also the basis algebraic geometry. paper, turned out to be the missing key. His of the theory of holomorphic symplectic conjecture says that the so-called Unique varieties, which have been intensely studied Subhash Khot’s most celebrated work, Games problem, a mild variant of the in recent years, as they encode highly and the one that led to his recent Nevanlinna standard NP-complete constraint satisfaction nontrivial algebraic integrable systems. Prize, is on the “Unique Games conjecture.” problem, is hard. So in order to show that a Bogomolov stability, Bogomolov-Miyaoka- […] The conjecture addresses the main problem is hard based on UGC, one needs to Yau inequality, Beauville-Bogomolov form, question in computational complexity: how show that it is as hard as the Unique Games

In Memoriam: Norman Grossman (November 3, 1922-May 29, 2015)

Dr. Norman years to earn his Ph.D., which he completed mph.” The relatively inexpensive Warthog, Grossman in 1958 with the dissertation “Nonlinear as it is known, was and remains a single- (Ph.D. ‘58), a Problems in Elastic Stability,” advised by Fritz seat plane that can fly for extended periods distinguished John. of time, at low altitudes, and with excellent alumnus of the At Fairchild Republic, Grossman maneuverability. It is extremely durable, Courant Institute, was responsible for design, production and accurate in weapons deployment, and spent his entire testing of high-performance military aircraft. capable of destroying armored vehicles career at the During his tenure there, the company such as tanks. Grossman was paraphrased Fairchild Republic secured many military contracts. One of the by Forbes as saying, “the plane is so Company in most well-known and long-lived was the A-10 resilient that it can lose an engine, 16 Farmingdale, jet, which was conceived in the early 1970s feet of a wing, and part of its tail, and still Long Island. as a strategic response to combat challenges return to base.” Some 700 A-10s have been Beginning as a junior engineer (at what in Vietnam, where the Air Force’s sleek, fast made. Though much beloved by its pilots was then Republic Aviation) and retiring as planes were not well suited to assisting and and arguably the most successful close air chairman and CEO, Grossman had only a providing cover to troops on the ground. First support aircraft in Air Force history, it has single, two-year absence in the 40s to serve deployed for combat in the Gulf War, a 1991 been threatened with mothballing over the in the Merchant Marine during World War II. Forbes article describes the A-10 as “Squat, years. It’s currently still scheduled to fly at After returning from the war, Grossman began heavily armored, with bulging jet engines least through 2022. attending the Courant Institute at night while perched high and to the rear of its boxy Despite knowing every nook and working full time at Republic. It took him 10 fuselage” and with a “peak speed of just 420 corner of the plane, Grossman didn’t ride

8 — CIMS Newsletter, Fall 2015 STUDENT HONORS problem. Using the UGC, one can show that Henning Biermann Prize Moses A. Greenfield Research Prize many natural optimization questions are Shravas Rao Nadejda Drenska hard. Moreover, one can often nail down Rahul Gopalkrishnan Martin and Sarah Leibowitz precisely the best approximation factor Sandra Bleistein Prize Graduate Prize achievable. In a series of remarkable papers Irena Vankova for Quantitative Biology by Subhash and others, it was then realized Benjamin Fogelson that for a large family of problems, the UGC Thomas Tyler Bringley Fellowship gives the precise approximability factors. Alexander Kaiser Wilhelm Magnus Memorial Prize Subhash Khot’s research has received Travis Askham Hollis Cooley Prize extraordinary levels of recognition and Insuk Seo Taher Dahleh honor. In 2014 he won the Rolf Nevanlinna Math Master’s Thesis Prize Prize, the highest scientific award in Janet Fabri Prize Chanyang Ryoo theoretical computer science, awarded once Jonathan Tompson every 4 years at the International Congress Sunandan Chakraborty Master’s Innovation Prize of Mathematicians, for outstanding OnYou Hwang Kurt O. Friedrichs Prize contributions in Mathematical Aspects Kavitha Vishwanathan Nan Chen of Information Sciences. In 2010 he was Nishant Kumar Ian Tobasco awarded the NSF Alan T. Waterman award, Matthew Smosna Prize given annually to a single scientist in the Paul Garabedian Fellowship Yi Wan U.S. aged 35 or younger. He was named a Emily Denton Prashant Singh Tewatia Simons Foundation Investigator in 2015. Max Goldstein Prize In 2010 he was an invited speaker at the Abhinay Ashutosh International Congress of Mathematicians. Congratulations to our 2016 Student He has received an NSF CAREER award, Harold Grad Memorial Prize Award Recipients! a Sloan Foundation Fellowship, and a Vitaly Kuznetsov Find out more about these awards Microsoft New Faculty Fellowship. n Moumanti Podder at http://cims.nyu.edu/academics/ Thien Nguyen student_recognition.html

inside of one until sometime in the 80s, when he got a call that an experimental two- seat Warthog at Edwards Air Force Base in southern California was waiting to take him up in the air. The pilot flew the plane blind, at night, and in between mountains. At the end of the flight, Grossman emerged (see photo) with watery eyes — happy to be back on the ground! “As quick with a smile as he was with the answer to a complex theoretical problem, Grossman was a rare bird in today’s world, a gentleman, a true scholar,” says the obituary printed in the New York Times. He was “one who lived his life with integrity and joy.” Grossman is survived by his wife Thelma, with whom he hosted several NYU alumni gatherings in their home in Greenwich Village, and by nieces Susan Scribner and Meryl Fiedelman. He passed away peacefully last spring at the age of 92. n

9 FACULTY HONORS

Courant Director Gérard Benarous was elected a Theodore Rappaport is the recipient of the 2015 IEEE member of the American Academy of Arts & Sciences, Communications Society Edwin Howard Armstrong one of the nation’s oldest and most prestigious honorary Achievement Award, “for broad contribution and societies. “Each new member is a leader in his or her outstanding leadership in channel measurement field and has made a distinct contribution to the nation and technology research fundamental to mobile and the world,” said Don Randel, chair of the Academy’s communication.” The Armstrong Achievement Award Board of Directors. recognizes “outstanding contributions over a period of years in the field of interest of the Society.” Richard Bonneau received the 2015 Iakobachvili Faculty Science Award from the NYU School of Arts and Dennis Shasha has been named an INRIA international chair, Science. The award recognizes “science faculty who’ve a research award given to approximately five international most clearly demonstrated evidence of past excellence researchers per year. He is hosted by the ZENITH project and future prospects of growth.” team in Montpellier, France, which focuses on designing algorithms for large scale scientific data problems. Subhash Khot has been named a Simons Investigator in Theoretical Computer Science by the Simons Victor Shoup has been named a Fellow of the International Foundation. As stated in their announcement, Subhash Association for Cryptological Resesearch, “for fundamental “initiated a new direction in computational complexity contributions to public-key cryptography and cryptographic theory and approximation algorithms, based on his security proofs, and for educational leadership.” He has Unique Games conjecture, which is currently one of the also been awarded the 2015 Richard D. Jenks Memorial most important conjectures in theoretical computer Prize by ACM’s SIGSAM (Special Interest Group in Symbolic science.” and Algebraic Manipulation) for Excellence in Software Engineering Applied to Computer Algebra for his work on Peter Lax received an Honorary Doctor of Science NTL: A Library for Doing Number Theory. degree from NYU for his contributions to Mathematics and the university. An alumnus and Professor Emeritus Georg Stadler and colleagues won the Association at the Courant Institute, Peter is also the recipient of the for Computing Machinery’s 2015 Gordon Bell Prize Abel prize in 2005, and recently went to Washington to in recognition of outstanding achievement in high- receive the Lomonosov Gold Medal, the highest award performance computing. The team received the prize for given by the Russian Academy of Sciences, which he the development of algorithms for solving large nonlinear was awarded in 2013. systems arising in geodynamics. The work is detailed in the paper An Extreme-Scale Implicit Solver for Complex Yann LeCun was awarded the IEEE PAMI (Pattern PDEs: Highly Heterogeneous Flow in Earth’s Mantle, and will Analysis and Machine Intelligence) Distinguished “[allow] researchers to gain new insights into the geological Researcher award at the 2015 International Conference evolution of the planet,’’ says the ACM. on Computer Vision. The award recognizes candidates “whose research contributions have significantly Duke University has awarded Raghu Varadhan an honorary contributed to the progress of Computer Vision.” degree, a Doctor of Science, honoris causa, citing his distinctions including the Abel Prize, awarded for “his Andrew Majda has received the American Mathematical contributions to probability theory and for creating a Society’s 2016 Leroy P. Steele Prize for seminal unified theory of large deviations,” and his National Medal of contributions to research. The award honors two 1983 Science. Duke President Richard H. Brodhead said: “These papers which, “To date, [remain] the only available degrees honor individuals who have made outstanding complete and general result about multidimensional contributions in diverse fields. We lift them up as inspiring systems” of conservation laws, “which are fundamental examples of how today’s graduates might use their talent in fluid mechanics,” writes the AMS. The papers —The and education to make their own contributions to the existence of multidimensional shock fronts and The world.” stability of multidimensional shock fronts — “pioneered the expansion” of research in this area from the one- Fedor Bogomolov and Subhash Khot were also named dimensional to the multi-dimensional case. Silver Professors (see page 8).

10 — CIMS Newsletter, Fall 2015 Math outreach champion: Fred Greenleaf retires, but doesn’t slow down

by April Bacon

those spaces. This work with Larry Corwin school students attend Courant courses. One began when Larry was a postdoc at Courant student, who graduated this year, “has ten and extended over 20 years until 1992, graduate math courses under his belt,” says when Larry died unexpectedly. Fred. “He’s ready to start dissertation work. After one more semester, he’ll work with an An Anchor for Math Outreach advisor, pick a topic and start reading the and Education literature.” Fred’s focus on math education Fred has also had successes in some began in 1990, when, as chairman of NYU’s mathematics policy reform. Fred and David Science Education Policy Committee, he Garbasz met around 2000 through New York led development of the math and science Hold, an organization of concerned parents curriculum required of all non-science and educators. Garbasz, an entrepreneur and majors. In 1993 he continued to steer reform philanthropist who gave seed money for the of large-scale core education through NSF- CMT, says that, as two examples, Fred was Professor Fred Greenleaf retired in funded NYU initiatives, leading a team of “instrumental” in getting a more rigorous January after 48 years at Courant. For the faculty that included the Chairs of all Science math curriculum adopted in Israel and in past 25 plus years at the Institute, he has Departments. Together they created the convincing the selective New York City NEST been dedicated to mathematics outreach Math and Science components of the Morse school to adopt Singapore math, which and education. The number of students Fred, Academic Plan (MAP). “I got to work with a emphasizes mastery of math content. winner of two NYU Golden Dozen Awards for lot of people in many different fields,” says Later, Garbasz’s mathematically Distinguished teaching, has reached, extends Fred, whose multi-disciplined background talented daughters took coursework with well beyond those who took his classes. made him well-suited for the role. MAP Fred when they were in high school. “He In 1955, as a high school student, provides a solid foundation for students in was always very welcoming,” Garbasz says. Fred was the Westinghouse Science Talent answering questions like: How do we know “When one of my daughters was studying Search Grand Prize winner across all of the what we know about the universe? How can algebra with him, he gave her a dozen sciences for a project in his original area of we use mathematical tools to find out how it textbooks off his walls. He’s a very generous interest—chemistry. As an undergraduate works? guy, a very good mathematician, and a great at Pennsylvania State University, he Fred’s many contributions to math teacher,” he says, lamenting that Fred is studied chemistry, physics and math in education are difficult to summarize because retiring. The silver lining: “Fred’s still very an Engineering Physics program and they are so numerous: He has written active. I doubt he’ll slow down.” his master’s NSF fellowship at Yale was textbooks and course notes, designed In retirement, Fred will continue to in biophysics. In the middle of his first curricula, and mentored high school and advise and participate in the CMT. They semester of graduate studies he transferred undergraduate students. He’s played a plan to expand the number of high school to the Ph.D. program in Mathematics, as part in cSplash, NYC Math Circles, and students attending Courant classes as an NSF Fellow. He completed his Ph.D. Courant’s Center for Mathematical Talent well as develop programs for “NYC middle (Mathematics) at Yale in 1964. After a year as (CMT). He served as chief advisor for the school students who would benefit from an instructor at UC Berkeley, he became an Math for America Fellows at NYU, a joint enrichment programs,” says Fred. He has Assistant Professor there. Three years later, in program with Steinhardt that trained highly been collaborating with Fedor Bogomolov 1968, he came to NYU. gifted high school math teachers. “He was on lecture notes for graduate Algebra I and Fred’s research in the 70s and early 80s invaluable for the students going through II. “Being retired, I actually have time to focused on geometry of groups, says Martin that program,” says Courant Professor think about this stuff more!” he says. He Moskowitz (CUNY), a longtime collaborator Sylvain Cappell, “as a mentor, as a teacher, also meets regularly with Moskowitz to work of Fred’s. “We studied the set B(G) of and as a person who helped shape the on questions about lattices and discrete bounded conjugacy classes in a Lie group program.” Additionally, says Sylvain, “Fred subgroups. G and proved it is closed (quite unexpected), supported high quality high school teachers “As my wife says, ‘How will they know and is precisely the union of supports of the when they were facing people that wanted a he’s retired? He’s still got an office and his finite G-invariant measures,” says Moskowitz. watered-down math curriculum.” computer account. He lives two blocks away. Later Fred began investigations applying Parents also concerned about K-12 He’s over there all of the time,’” says Fred. As Kirillov’s “method of coadjoint orbits’’ to math education have called the Institute Sylvain expresses, we hope for many years break new ground in representations of for decades. Fred has been a central part that Fred will “continue in his involvement, nilpotent Lie groups, noncommutative in initiatives designed to provide those because of his wisdom, his deep concern, harmonic analysis on their homogeneous students with opportunities they need yet deep knowledge and understanding of the spaces, and structure and solutions of are not necessarily getting in their schools. issues involved in mathematics education.” invariant differential operators that live on Through the CMT, for example, talented high

11 Like family: Larry Cohen, tireless staff member, retires

by April Bacon

asking him to stay a little longer,” says Irene Robling, Associate Director of Administration and Finance at Courant. “For most of us, we’ve never been at Courant without him and he will be missed by everyone, especially those who will no longer be able to find Larry before 7am to copy finals or midterms!” “Larry Cohen has been at the Courant Institute for 41 years,” remarks Dave McLaughlin, NYU Provost and Professor of Mathematics and Neuroscience. “For the entire 41 years, Larry has been an integral part of the Courant community, always going above and beyond in the performance of his duties at the Institute.” In 2000, Larry was recognized for that service with an NYU Violet Award. He also received an award for never being late on the job, a distinction he has maintained for the entirety his service — arriving not only on time, but an hour and a half early each day. “I’ve always had bosses tell me, you’re starting too early! You’re spoiling everybody!” says Larry, “And it does my heart well to do that. I’m here. I’m here for the people.” Larry has many happy memories from over the years. Peter Lax and Louis Nirenberg still visit Larry on occasion to reminisce about “the good old days” and to remember dear friends who have passed on, like Professors Paul Garabedian, Harold Grad, and longtime Instructor Samuel Marateck. Remembering those times “keeps us young,” says Larry. One personal memory with Sam Marateck began in their youth: In the early ’60s, Larry and Sam lived across the street from one another in Long Beach, and the two Larry Cohen, Duplicating and Mail Services Coordinator, is used to go surfing together. And in Larry’s earlier years at Courant, retiring after just over four decades at the Courant Institute. Larry, when dancing was a common feature of the Institute’s parties, Larry a Vietnam veteran, was trained in software by CDI (Control Data and his wife and children would join Professors Lax, Nirenberg, Institute) and in 1975, after returning from the military, he was hired and Garabedian and their wives, as well as other faculty and by Paul Garabedian to serve as the third shift operator for Courant’s administrators on the dance floor. CDC 6600. After nearly a year keeping the computer in operating Over the years, both of Larry and Sheri’s children, Staci and condition, Larry requested to move into a daytime role at the Institute Matthew, earned degrees from NYU’s Stern School of business. Larry so that he could preserve his evenings for his family—his wife, Sheri, also got to see the Courant Institute’s students earn their degrees, and his daughter on the way. While on his first vacation for the birth graduate, and come back to visit the Institute years later as “deans of his daughter, Staci, Larry recalls receiving a call from his supervisor and chairpersons” at other Universities. who said: “I have good news and I have bad news — the good news “It was like family here,” Larry says. is you can have a day job if you want it. The bad news is you have to After retirement, Larry will be moving from his home in Forest Start ASAP!” Hills to Laguna Hills, California. He and his wife will live near their With that phone call, Larry began his service to the Institute in two children and grandsons Jake (13), Max (12), and Noah (5), and the role in which so many faculty, students, and administrators have in May will be celebrating the arrival of their fourth grandson. Their come to depend on him. There are few who have passed through the children are naturally thrilled about the move—“and not just for Institute who haven’t heard Larry’s five reassuring words: “I’ll take the babysitting!” says Larry, “But for all of us to be together — that’s care of it.” While the days of typing, copying and shipping cartons important with a family. It’s time, after 41 years, to make time for my of proposals for grant applications are, thankfully, long gone, Larry’s children. To live out the rest of my life. And take up surfing again!” contributions to daily operations continue to be essential to life at With his parting message, Larry offers: “I’ll always remember Courant. Mail correspondence arrives to its destinations on time, mail everybody here [at Courant]. Everybody has a place in my heart. Boy, for Warren Weaver Hall occupants is delivered directly to mailboxes let me tell you: The years go fast. They really do. But I’ll tell you, they on the ground floor, the implements of daily Institute life are always were beautiful years here. Good years.” in supply, and thousands upon thousands of exam copies get safely “Larry will be missed by all,” concludes Dave. “And while we all made, even if an out-of-service copier means Larry has to run the job wish him the very best in retirement, it is hard to image the Courant across campus to get it done on time. “In recent weeks, I’ve overheard Institute without him.” n many faculty wondering what will happen after Larry retires and

12 — CIMS Newsletter, Spring 2016 A lot of heart: Tamar Arnon, student advocate, retires by April Bacon

Before a graduate student in mathematics arrives to the Courant Institute, one of the first names they come to know is Tamar Arnon, Assistant Director of Student Affairs. Tamar arrived at Courant in 1986, after about half a decade in the Office of the Dean of the Fac- ulty of Arts and Science. She served one semester in computer science before moving to the mathematics department. Now retiring after 30 years of service to the Institute, Tamar has seen many generations of students come through Warren Weaver Hall, easing the path of each one from admittance to graduation. Nadia Drenska, a fourth-year Ph.D. student studying optimal control theory and advised by Bob Kohn, recalls well her visit to the Institute after being admitted. Tamar had arranged meetings for her with seven faculty members in one day. “It was kind of overwhelm- ing!” exclaims Nadia—“but it was exactly what I needed to get a feel “It’s a collective memo of how we feel about her,” says graduate for the department.” student Nadia Drenska of this poster which Tamar displays in her office. Students made the gift for Tamar in spring 2014, when she Originally from Bulgaria, Nadia sought out Tamar again on was battling breast cancer for the second time. “I fought hard to several occasions. Once, as president of the Student Association, she come back as fast as my little legs would carry me,” says Tamar, needed help implementing a student mentor program for the next in- “because here is where all the good things happen to me.” coming class of students. “We wouldn’t have been able to implement this if she weren’t so willing to help out,” says Nadia. “You can see she really cares about you and she really wants to help… She’s been a sort difficult for them. Sometimes they don’t quite feel secure, the pressure of mother figure to us.” gets to them, the difficulty of doing a graduate degree, being away Students go to Tamar with any number of questions, asking from home — and there I am. And I can bring them up and out. And for guidance on and assistance with, for example, things like what this is one of the things that I treasure.” courses to select, when to find a faculty mentor, how to organize an Although her work prior to arriving at Courant was pleasant event, and for broader general advice such as on how to be an effec- enough, something about the Institute was different for her. Before tive teacher. With some English as a second language students, Tamar Courant, “I didn’t have in my career anything that was central to my has even put in extra hours coaching them through classics. As a lover life, that gave me a real purpose,” she says. At Courant, she was able to of great literature, she has guided them through works like Harper answer the questions, “‘What do I do with my day?’ And, ‘What I do, Lee’s To Kill a Mockingbird, John Steinbeck’s East of Eden and, for how does it matter’? … I think that what we do here matters a great young women, Louisa May Alcott’s Little Women. Regardless how big deal, to individual people and to the cause of education.” or small the issue, Tamar is always there, eager to listen and help. “Until I came to Courant,” Tamar says, “I’d never really been “Everybody knows her impact with students is enormous,” says able to use my brain on the job. When I came here, the faculty asked Melissa Kushner Vacca, Manager of Academic Affairs for the math de- me for really the first time, the all important question: ‘Tamar, what partment, who has been with the Institute for ten years. For Melissa, do you think?’ And I almost died. I’d never been asked that before. one moment in particular characterizes perfectly Tamar’s commit- And since then they’ve spoiled me into becoming a thinking person ment to students: the morning of one prospective Ph.D. student and now they hear what I think whether they want to hear it or not!” visit, when Tamar called Melissa into her office. “She’s sitting in her What is immensely evident is that her advice is wanted, and office with a scarf wrapped around her arm, holding herbroken wrist sought out by students, faculty, and administrators alike. “There are up. And she looks at me very seriously and says: ‘I think I may need so many times that we will run to her — her advice is so valuable. Her to go to the emergency room but I needed to come and meet these impact will be felt even after she’s gone,” says Melissa. “I can speak on students today’! behalf of all of the staff here that we will miss her enormously.” “Her dedication is so evident,” Melissa says. “She’s come in Tamar returns the affection. “We have a team here [in the through injury, through illness. She fights her way back in.” math department] of several women [administrators],” she says. Nadia’s experience and Melissa’s story are emblematic of the “We’re ‘all for one, one for all.’ It’s really neat when, as a team, we dedication and heart that, in 2000, earned Tamar an NYU Distin- come up with something creative to solve [a student’s] problem… guished Administrator Award. it really makes your day when you see these students who ran into “I know it must be very hard to finish a graduate degree,” says trouble persevere.” Tamar, “and I want to be there. I always think of myself as holding What will Tamar do when she leaves the Institute? “One thing a giant broomstick, running a little bit ahead of them and clearing I’ll be doing is the day after I leave, I come right back!” she says. “I’ll the path as much as I can — all the little things. Every once in a blue be working part time so that I have a softer landing.” After that, “One moon a big thing. But all the little things that are going to make it [idea] is to be a lady of leisure in New York City. I can’t think of a better

13 thing. I love museums and theater and opera and ballet. But some- the idea of any other Tamar is not easy for me. It’ll happen. thing will be missing just doing that, there’s no question. So, working “A lot of heart goes into this,” says Tamar. “It’s been good or volunteering with young people. Maybe with people who need for me. Working here really gave me a focus about what is impor- help with English as a foreign language. There are a lot of possibilities tant and how all of us in our own way can be part of something and I hate to admit, but I haven’t explored them yet because I’ve been much bigger.” n Tamar from Courant for such a long time and loving it so much that

PUZZLE SPRING 2016

Sleep No More Solution to Second Warm-up by Dennis Shasha Recall (y—x) mod 60 = y — x if x < y or (y+60) — x, Professor of Computer Science otherwise; for example, (14—4) mod 60 = 10, but (4—14) mod 60 = 50; (y—x) mod 60 is thus the number of minutes on the 60-minute clock that value y is ahead of x. Let L2 be the minimum non-negative value having the property m = (A — (T+L2)) mod 60. L2 is the number of ALARM HOUR ALARM MINUTE TIME HOUR TIME MINUTE minutes we would have to advance the time to achieve our goal of waking up in m minutes. We call it timeadvance and solve for it as follows: timeadvance(A, T, m) = (A — (T+m)) mod 60. 151: 8 If timeadvance(A, T, m) <= 30, then advance the time by that amount, else advance the alarm by 60 — timeadvance 14:20 (A, T, m). End of solution. Now imagine you have a 24-hour clock for both alarm and time. You have the same problem. You want the alarm to go off in m minutes where m can now be any number up to (24 x 60) — 1 minutes. As with every alarm clock, this one can hardly You can move the hour value (between 0 and 23) wait to ring, and you must figure out how to set it to wake you up when your nap is over, making for both time and alarm separately from the minute value as few button pushes as possible. (between 0 and 59). Each move forward by one of any hour or minute counter costs one unit of effort. (Moving the minute value past 59 to 0 does not affect the hour value.) Is it ever an advantage to move both a time value and an We begin simply, with a 60-minute clock that counts only alarm value, as opposed to just one? minutes, going from 0 to 59. The alarm can also be set from 0 to 59 and will go off when the clock reaches the same value. Say you want Solution the alarm to go off in m (m < 60) minutes, the time value now is x, and the alarm value is y. You want to move the time value or alarm Yes. Suppose the time is set at 15:18 and the alarm is value forward as little as possible so the alarm goes off m minutes 14:50. You want the alarm to go off in 30 minutes. The best from now. thing is to move the alarm forward by one hour and the time to 15:20, costing a total of three units of effort. Can you now find an elegant solution, that is, by WARM-UP The time is at 20 minutes, and the alarm is at 5 minutes. You want the alarm to go off in 35 minutes. One possibility is minimizing the case analysis and figuring out a cost- to move the alarm forward (the only allowable direction) to 55. minimizing algorithm for this problem? Your alarm clock will Another is to move the time value ahead to 30. The second solution still have the pleasure of waking you up, but it will never know is less expensive, requiring only 10 pushes, so you prefer that. what time it really is.

Dennis Shasha is a professor of computer science in the SECOND WARM-UP In general, for this 60-minute clock, if T is the time value and A is the alarm value and you want to wake up in m (< Courant Institute at New York University, New York, as well as 60) minutes, which value do you move and at what cost in terms of the chronicler of his good friend the omniheurist Dr. Ecco. number of minutes ahead you must push that value?

14 — CIMS Newsletter, Spring 2016 EVENTS AT COURANT

Jun Zhang, Courant Professor and Co-director of the Applied Math Lab (AML), presented this year’s Holiday Lecture on “The Little Lab in the Lobby,” discussing the history and complexities of fluid dynamics and experiments conducted in the AML. As Courant Director Gérard Benarous said in his opening remarks, “Jun’s work is well known for its creativity, its The Institute presented a discussion for alumni and friends flare, and its elegance, whether it’s flags flapping, fish , on global sea level rise on February 24. Here, Center for or cyclic motions of the earth’s continents, his experimental Atmosphere and Ocean Science Professor David Holland work has inspired many people across the world.” Watch this (right) speaks with Jack Cogen (MS’82, MBA ’87). Holland was and other holiday lectures at http://video.cims.nyu.edu/media/ joined by Professors Dale Jamieson, Chair of Environmental HolidayLectures/. Studies, and Michael Oppenheimer of NYU’s Law School and Princeton’s Woodrow Wilson School. A Challenge to Double the Impact THE GENEROSITY OF FRIENDS of Your First Gift to Courant!

Tuition and fees do not cover the true cost of education. Donations from alumni, friends and others who believe in $235,000 the importance of education and research provide support Fiscal year 2016 ends August 31. for the Courant Institute’s mission and are critical to its Our Annual Fund goal is $235,000. remaining competitive with its historically well-endowed Please give today! peers. Private support makes possible scholarships and fellowships and adds resources for research facilities like $147,000 the Applied Math Lab. They enable the Institute to invite distinguished speakers for both technical and public lectures, and assist in maintaining an up-to-date learning environment. They also support student clubs such as Women in Computing (WinC), alumni social and professional networking events and community outreach programs like Please use the enclosed return The Center for Mathematical Talent which provides math envelope or give securely on-line at enrichment to New York City elementary, middle and high www.nyu.edu/giving/courant. school kids — many from underserved communities — and the GSTEM girls’ summer STEM internship program.

We are deeply grateful to our all our donors, which is why we Did you know that alumni participation in giving affects university initiated the Sigma Society in the Fall of 2015 to recognize rankings? To demonstrate their commitment to Courant and to those who have given a gift of any size in each of the last five encourage giving in any amount from all Courant alumni, several years. Giving is extremely personal but we hope that if you are loyal and generous alumni are offering a special challenge. For the in a position to give special support, that you will consider remainder of fiscal year 2016, they have pledged to match the gifts contributing at the Director’s Circle level of $1,000 or more, of all first time donors 1:1 up to a total of $30,000! So if you give for or contact the Development Office to find out about the the first time between now and August 31, your gift will be worth Institute’s specific needs. Donors at the $2,500 level are also twice its face value. invited to join the NYU Society and at the $5,000 level the President’s Council. Visit matchinggifts.com/nyu/ to see if your employer matches your gifts to education. DONOR ACKNOWLEDGEMENT

The annual list of donors to the Institute will appear in our Fall 2016 issue. Make your gift conveniently and securely online at www.nyu.edu/giving/Courant and visit matchinggifts.com/nyu/ to see if your employer matches your gifts to education.

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Send us news of job changes, moves, and meet-ups with Courant Courant Newsletter Staff: alums at [email protected]. We also invite all Alumni Editors: Robin Roy and Shafer Smith to keep colleagues and friends up-to-date on life events such as career Writer and Managing Editor: April Bacon achievements and family milestones; submitted items will be considered Graphic Designer: Chris Cantley for publication in the Newsletter or online.

Please make sure your contact information is up to date by Dynamical systems visiting the NYU Alumni website at www.nyu.edu/alumni or studies have advanced send your email and postal address, phone or employment changes to considerably since [email protected] and we’ll take care of the rest. Edward Lorenz’s butterfly attractor There are benefits to being an NYU alumnus/a. Check out the NYU (at left) first offered Alumni webpage for campus and library access, insurance, entertainment a point of entry for and dining, university club memberships in your area, and much more, understanding them including NYU alumni networking events wherever you go! (see page 2).